# How do you simplify -6/(5-sqrt11)?

Mar 22, 2017

$- \frac{30 + 6 \sqrt{11}}{36}$

#### Explanation:

rationalise the denominator.

use this law:
$\left(a + b\right) \left(a - b\right) = {a}^{2} - {b}^{2}$

to rationalise $5 - \sqrt{11}$, multiply it by $5 + \sqrt{11}$:

$5 + \sqrt{11} \cdot 5 - \sqrt{11} = {5}^{2} + {\left(\sqrt{11}\right)}^{2}$

$= 25 + 11$

$= 36$

multiply the numerator by $5 + \sqrt{11}$ as well:

$6 \cdot \left(5 + \sqrt{11}\right) = 30 + 6 \sqrt{11}$

fraction: $- \frac{30 + 6 \sqrt{11}}{36}$